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A one-meter long bar is heated unevenly, with temperature in °C at a distance x meters trom one end at time t given by H(x, t) = 100e-0.05t sin(Tx) 0 < « < 1. On a sheet of paper, sketch a graph ofH against a for t = 0 and t = 1. Think about why your graphs make sense. (a) Calculate each of: H(0.1, t) = H,(0.9, t) = (Be sure that you can say in words what the practical interpretation (in terms of temperature) of these two partial derivatives is, and why each has the sign that it does.) (b) Calculate: H(x, t) = %3D (Again, be sure that you understand why it has the sign that it does, and what its interpretation in terms of

A one-meter long bar is heated unevenly, with temperature in °C at a distance x meters trom one end at time t given by H(x, t) = 100e-0.05t sin(Tx) 0 < « < 1. On a sheet of paper, sketch a graph ofH against a for t = 0 and t = 1. Think about why your graphs make sense. (a) Calculate each of: H(0.1, t) = H,(0.9, t) = (Be sure that you can say in words what the practical interpretation (in terms of temperature) of these two partial derivatives is, and why each has the sign that it does.) (b) Calculate: H(x, t) = %3D (Again, be sure that you understand why it has the sign that it does, and what its interpretation in terms of

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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A one-meter long bar is heated unevenly, with temperature in °C at a distance x meters from one end at time t given by H(x, t) = 100e-0.05t sin(ræ) 0 < « < 1. On a sheet of paper, sketch a graph of H against a for t = 0 and t = 1. Think about why your graphs make sense. (a) Calculate each of: H (0.1, t) H (0.9, t) = (Be sure that you can say in words what the practical interpretation (in terms of temperature) of these two partial derivatives is, and why each has the sign that it does.) (b) Calculate: H(x, t) (Again, be sure that you understand why it has the sign that it does, and what its interpretation in terms of g0 F3 I F8 F6 F7 F10 F11 F4 FS F9 2$ % & * + 4 5 6 7 8 { R Y U F G H K V N alt command option .. .. V ーの B ト
Transcribed Image Text:A one-meter long bar is heated unevenly, with temperature in °C at a distance x meters from one end at time t given by H(x, t) = 100e-0.05t sin(ræ) 0 < « < 1. On a sheet of paper, sketch a graph of H against a for t = 0 and t = 1. Think about why your graphs make sense. (a) Calculate each of: H (0.1, t) H (0.9, t) = (Be sure that you can say in words what the practical interpretation (in terms of temperature) of these two partial derivatives is, and why each has the sign that it does.) (b) Calculate: H(x, t) (Again, be sure that you understand why it has the sign that it does, and what its interpretation in terms of g0 F3 I F8 F6 F7 F10 F11 F4 FS F9 2$ % & * + 4 5 6 7 8 { R Y U F G H K V N alt command option .. .. V ーの B ト
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